Finite Group Databasebeta

← #27204975

Subgroups — #27204975

Order 13184.

398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268419C211yesmaximal, characteristic, complemented
2#20268091C212yesmaximal, complemented
3#20268091C212yesmaximal, complemented
4#20268081C212yesmaximal, complemented
5#20268071C212yesmaximal, complemented
6#20267834C211yesmaximal, characteristic, complemented
7#20267827C211yesmaximal, characteristic, complemented
8#20267818C211yesmaximal, characteristic, complemented
9#20267796C211yesmaximal, characteristic
10C2×#15692942C211yesmaximal, characteristic
11#518×C103C211yesmaximal, characteristic
12C2×#13110089C2211yescharacteristic
13C22×C103⋊C8C2211yescharacteristic
14#15693021C2212yescomplemented
15#15693020—21no—
16#15693013C2212yescomplemented
17#15693012—21no—
18#15692998—22no—
19#15692980C2211yescharacteristic
20C2×C4⋊Dic103C2211yescharacteristic
21#15692954C2211yescharacteristic, complemented
22#15692954C2212yescomplemented
23#15692954C2211yescharacteristic, complemented
24#15692952C2211yescharacteristic, complemented
25#15692952C2212yescomplemented
26#15692952C2211yescharacteristic, complemented
27C4⋊(C103⋊C8)C2212yescomplemented
28C4⋊(C103⋊C8)C2212yescomplemented
29#15692942C2212yes—
30#15692942C2212yes—
31#15692942C2212yes—
32#15692942C2212yes—
33C22×D4×C103C2211yescharacteristic
34C4×D4×C103—21no—
35C4×D4×C103—21no—
36C4×D4×C103C2212yes—
37C4×D4×C103C2212yes—
38#117×C103C2211yescharacteristic
39#117×C103C2211yescharacteristic
40C2×C22⋊C4×C103—22no—
41C2×Dic206—22no—
42C22×Dic103—21no—
43#13110089—22no—
44C2×C103⋊C8—22no—
45C2×C103⋊C8C2311yescharacteristic
46C2×C103⋊C8C2312yes—
47C2×C103⋊C8C2311yescharacteristic
48C4⋊Dic103—21no—
49C4⋊Dic103—22no—
50C4⋊Dic103C2312yes—
51C4⋊Dic103C2311yescharacteristic
52C4⋊Dic103C2311yescharacteristic
53Dic103⋊C4—22no—
54Dic103⋊C4—22no—
55C22⋊Dic103—21no—
56C4×Dic103—21no—
57C24×C103—21no—
58C2×D4×C103—21no—
59C2×D4×C103—22no—
60C2×D4×C103Q814yescomplemented
61C2×D4×C103C2312yes—
62C22×C4×C103—22no—
63C22×C4×C103—22no—
64C22×C4×C103C2311yescharacteristic
65C4⋊C4×C103D411yescharacteristic
66C4⋊C4×C103D411yescharacteristic
67C4⋊C4×C103C2311yescharacteristic
68C4⋊C4×C103C2311yescharacteristic
69C22⋊C4×C103—21no—
70C22⋊C4×C103—22no—
71C22⋊C4×C103—22no—
72C22⋊C4×C103D412yes—
73C42×C103—21no—
74C42×C103C2312yes—
75C23×C103—22no—
76C23×C103—24no—
77C23×C103—81no—
78C23×C103—81no—
79C23×C103C2×D411yescharacteristic
80D4×C103—24no—
81D4×C103—22no—
82D4×C103C2×Q814yes—
83C2×C4×C103—21no—
84C2×C4×C103—21no—
85C2×C4×C103—82no—
86C2×C4×C103—82no—
87C2×C4×C103C2×D412yes—
88C2×C4×C103C2×D412yes—
89C2×C4×C103C2×D411yescharacteristic
90C2×C4×C103C2×Q812yes—
91C2×C4×C103#4112yes—
92C2×C4×C103C2411yescharacteristic
93C2×Dic103—21no—
94C2×Dic103—21no—
95C2×Dic103—22no—
96C2×Dic103—81no—
97Dic206—82no—
98C103⋊C8—21no—
99C103⋊C8—21no—
100C103⋊C8—22no—
101C22×C103—21no—
102C22×C103—21no—
103C22×C103—24no—
104C22×C103—42no—
105C22×C103—42no—
106C22×C103—84no—
107C22×C103C22⋊Q812yes—
108C22×C103C22×D411yescharacteristic
109C4×C103—22no—
110C4×C103—22no—
111C4×C103—41no—
112C4×C103—41no—
113C4×C103C22⋊Q812yes—
114C4×C103C22×Q811yescharacteristic
115C4×C103C2×#4111yescharacteristic
116Dic103—41no—
117Dic103—42no—
118Dic103—41no—
119C2×C103—22no—
120C2×C103—44no—
121C2×C103C2×C22⋊Q811yescharacteristic
122C2×C103#57611yescharacteristic
123C2×C103#57711yescharacteristic
124#3081—1031nomaximal, Sylow
125C103#308111yescharacteristic, complemented, Sylow
126#544—1031no—
127#518D10311yescharacteristic
128#478—1032no—
129#478—1032no—
130#476—1032no—
131#474—1032no—
132#428—1031no—
133#427—1031no—
134#424—1031no—
135#418—1031no—
136C2×#102—1031no—
137C22×D4C2×D10311yescharacteristic
138C2×M16—1031no—
139C22×C8—1031no—
140C4⋊Q8—1032no—
141C4⋊Q8—2061no—
142#125—1032no—
143#125—2061no—
144C22⋊Q8—2062no—
145C4×D4—21no—
146C4×D4—21no—
147C4×D4C2×D10312yes—
148C4×D4C2×D10312yes—
149#117—1031no—
150#117C2×D10311yescharacteristic
151#117C2×D10311yescharacteristic
152C2×C4⋊C4—1031no—
153C2×C22⋊C4—22no—
154#107—1031no—
155#107—1031no—
156#107—1032no—
157#106—1031no—
158#106—1031no—
159#106—1032no—
160C4⋊C8—1032no—
161C4⋊C8—1032no—
162#102—1032no—
163#102—1032no—
164#102—1032no—
165#102—1032no—
166C24—21no—
167C2×Q8—2062no—
168C2×D4—21no—
169C2×D4—22no—
170C2×D4Dic20614yescomplemented
171C2×D4C22×D10312yes—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—2061no—
175C22×C4C22×D10311yescharacteristic
176M16—2062no—
177C2×C8—1031no—
178C2×C8—1032no—
179C2×C8—1031no—
180C2×C8—2062no—
181C4⋊C4—1032no—
182C4⋊C4—1031no—
183C4⋊C4—1031no—
184C4⋊C4—2062no—
185C4⋊C4—2062no—
186C4⋊C4—2061no—
187C4⋊C4—2062no—
188C4⋊C4C22⋊D10311yescharacteristic
189C4⋊C4C22⋊D10311yescharacteristic
190C4⋊C4C22×D10311yescharacteristic
191C4⋊C4C22×D10311yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—22no—
194C22⋊C4—22no—
195C22⋊C4—2061no—
196C22⋊C4C22⋊D10312yes—
197C42—21no—
198C42—2061no—
199C42C22×D10312yes—
200C23—22no—
201C23—24no—
202C23—81no—
203C23—81no—
204C23C2×C22⋊D10311yescharacteristic
205Q8—8242no—
206D4—22no—
207D4—24no—
208D4C2×Dic20614yes—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—82no—
212C2×C4—82no—
213C2×C4—8241no—
214C2×C4—2061no—
215C2×C4—2061no—
216C2×C4—2062no—
217C2×C4C2×C22⋊D10312yes—
218C2×C4C2×C22⋊D10312yes—
219C2×C4C2×C22⋊D10311yescharacteristic
220C2×C4C2×Dic20612yes—
221C2×C4#1311010512yes—
222C2×C4C23×D10311yescharacteristic
223C8—2061no—
224C8—2061no—
225C8—2062no—
226C22—21no—
227C22—21no—
228C22—24no—
229C22—42no—
230C22—42no—
231C22—84no—
232C22#1569300012yes—
233C22C22×C22⋊D10311yescharacteristic
234C4—22no—
235C4—22no—
236C4—41no—
237C4—41no—
238C4—4122no—
239C4—4121no—
240C4—4121no—
241C4#1569300012yes—
242C4C22×Dic20611yescharacteristic
243C4C2×#1311010511yescharacteristic
244C2—22no—
245C2—44no—
246C2C2×#1569300011yescharacteristic
247C2#2026859411yescharacteristic
248C2#2026860211yescharacteristic
subgroupG/H
centerC22C22×C22⋊D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#518×C103C2
socleC22×C103C22×D4
prime radicalC22×D4×C103C22
hypercenter#518D103
hypocenterC103#3081
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20268419C2semidirect
2. #20268091C2semidirect
3. #20268091C2semidirect
4. #20268081C2semidirect
5. #20268071C2semidirect
6. #20267834C2semidirect
7. #20267827C2semidirect
8. #20267818C2semidirect
14. #15693021C22semidirect
16. #15693013C22semidirect
21. #15692954C22semidirect
22. #15692954C22semidirect
23. #15692954C22semidirect
24. #15692952C22semidirect
25. #15692952C22semidirect
26. #15692952C22semidirect
27. C4⋊(C103⋊C8)C22semidirect
28. C4⋊(C103⋊C8)C22semidirect
60. C2×D4×C103Q8semidirect
125. C103#3081semidirect
170. C2×D4Dic206semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202684192
#202680912
#202680812
#202680712
#202678342
#202678272
#202678182
#202677962
C2×#156929422
#518×C1032
#3081103